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Zero Set
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Geliefert zwischen Mo., 26.01.2026 und Di., 27.01.2026
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High Quality Content by WIKIPEDIA articles! In mathematics, the zero set of a real-valued function f : X R (or more generally, a function taking values in some additive group) is the subset f 1(0) of X (the inverse image of 0). In other words, the zero set of the function f is the subset of X on which f(x) = 0. The cozero set of f is the complement of the zero set of f (i.e. the subset of X on which f is nonzero). Zero sets are important in several branches of geometry and topology. In differential geometry, zero sets are frequently used to define manifolds. An important spacial case is the case that f is a smooth function from Rp to Rn. If zero is a regular value of f then the zero-set of f is a smooth manifold of dimension m=p-n by the regular value theorem. For example, the unit m-sphere in Rm+1 is the zero set of the real-valued function f(x) = x 2 - 1.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131213618
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131213618
- Format Fachbuch
- Titel Zero Set
- Herausgeber Betascript Publishing
- Anzahl Seiten 124
- Genre Mathematik
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